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Relevant bibliographies by topics / Powers of monomial ideals

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Academic literature on the topic 'Powers of monomial ideals'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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Journal articles on the topic "Powers of monomial ideals"

1

Cooper, Susan M., Robert J. D. Embree, Huy Tài Hà, and Andrew H. Hoefel. "Symbolic Powers of Monomial Ideals." Proceedings of the Edinburgh Mathematical Society 60, no. 1 (2016): 39–55. http://dx.doi.org/10.1017/s0013091516000110.

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AbstractWe investigate symbolic and regular powers of monomial ideals. For a square-free monomial ideal I ⊆ 𝕜[x0, … , xn] we show that for all positive integers m, t and r, where e is the big-height of I and . This captures two conjectures (r = 1 and r = e): one of Harbourne and Huneke, and one of Bocci et al. We also introduce the symbolic polyhedron of a monomial ideal and use this to explore symbolic powers of non-square-free monomial ideals.

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Murai, Satoshi. "Borel-plus-powers monomial ideals." Journal of Pure and Applied Algebra 212, no. 6 (2008): 1321–36. http://dx.doi.org/10.1016/j.jpaa.2007.09.010.

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Altafi, N., N. Nemati, S. A. Seyed Fakhari, and S. Yassemi. "Free resolution of powers of monomial ideals and Golod rings." MATHEMATICA SCANDINAVICA 120, no. 1 (2017): 59. http://dx.doi.org/10.7146/math.scand.a-25504.

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Let $S = \mathbb{K}[x_1, \dots, x_n]$ be the polynomial ring over a field $\mathbb{K}$. In this paper we present a criterion for componentwise linearity of powers of monomial ideals. In particular, we prove that if a square-free monomial ideal $I$ contains no variable and some power of $I$ is componentwise linear, then $I$ satisfies the gcd condition. For a square-free monomial ideal $I$ which contains no variable, we show that $S/I$ is a Golod ring provided that for some integer $s\geq 1$, the ideal $I^s$ has linear quotients with respect to a monomial order.

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Seyed Fakhari, S. A. "Stanley depth and symbolic powers of monomial ideals." MATHEMATICA SCANDINAVICA 120, no. 1 (2017): 5. http://dx.doi.org/10.7146/math.scand.a-25501.

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The aim of this paper is to study the Stanley depth of symbolic powers of a squarefree monomial ideal. We prove that for every squarefree monomial ideal $I$ and every pair of integers $k, s\geq 1$, the inequalities $\mathrm{sdepth} (S/I^{(ks)}) \leq \mathrm{sdepth} (S/I^{(s)})$ and $\mathrm{sdepth}(I^{(ks)}) \leq \mathrm{sdepth} (I^{(s)})$ hold. If moreover $I$ is unmixed of height $d$, then we show that for every integer $k\geq1$, $\mathrm{sdepth}(I^{(k+d)})\leq \mathrm{sdepth}(I^{{(k)}})$ and $\mathrm{sdepth}(S/I^{(k+d)})\leq \mathrm{sdepth}(S/I^{{(k)}})$. Finally, we consider the limit beha

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Moradi, Somayeh, Masoomeh Rahimbeigi, Fahimeh Khosh-Ahang, and Ali Soleyman Jahan. "A family of monomial ideals with the persistence property." Journal of Algebra and Its Applications 18, no. 05 (2019): 1950093. http://dx.doi.org/10.1142/s0219498819500932.

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In this paper, we introduce a family of monomial ideals with the persistence property. Given positive integers [Formula: see text] and [Formula: see text], we consider the monomial ideal [Formula: see text] generated by all monomials [Formula: see text], where [Formula: see text] is an independent set of vertices of the path graph [Formula: see text] of size [Formula: see text], which is indeed the facet ideal of the [Formula: see text]th skeleton of the independence complex of [Formula: see text]. We describe the set of associated primes of all powers of [Formula: see text] explicitly. It tur

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Hernández, Daniel J., Pedro Teixeira, and Emily E. Witt. "Frobenius powers of some monomial ideals." Journal of Pure and Applied Algebra 224, no. 1 (2020): 66–85. http://dx.doi.org/10.1016/j.jpaa.2019.04.015.

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7

Hübl, Reinhold. "Powers of Elements and Monomial Ideals#." Communications in Algebra 33, no. 10 (2005): 3771–81. http://dx.doi.org/10.1080/00927870500242777.

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Seyed Fakhari, S. A. "On the Stanley Depth of Powers of Monomial Ideals." Mathematics 7, no. 7 (2019): 607. http://dx.doi.org/10.3390/math7070607.

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In 1982, Stanley predicted a combinatorial upper bound for the depth of any finitely generated multigraded module over a polynomial ring. The predicted invariant is now called the Stanley depth. Duval et al. found a counterexample for Stanley’s conjecture, and their counterexample is a quotient of squarefree monomial ideals. On the other hand, there is evidence showing that Stanley’s inequality can be true for high powers of monomial ideals. In this survey article, we collect the recent results in this direction. More precisely, we investigate the Stanley depth of powers, integral closure of p

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Banerjee, Arindam, Bidwan Chakraborty, Kanoy Kumar Das, Mousumi Mandal, and S. Selvaraja. "Regularity of powers of squarefree monomial ideals." Journal of Pure and Applied Algebra 226, no. 2 (2022): 106807. http://dx.doi.org/10.1016/j.jpaa.2021.106807.

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MIRANDA–NETO, CLETO B. "Analytic spread and non-vanishing of asymptotic depth." Mathematical Proceedings of the Cambridge Philosophical Society 163, no. 2 (2017): 289–99. http://dx.doi.org/10.1017/s0305004116001018.

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AbstractLetSbe a polynomial ring over a fieldKof characteristic zero and letM⊂Sbe an ideal given as an intersection of powers of incomparable monomial prime ideals (e.g., the case whereMis a squarefree monomial ideal). In this paper we provide a very effective, sufficient condition for a monomial prime idealP⊂ScontainingMbe such that the localisationMPhasnon-maximal analytic spread. Our technique describes, in fact, a concrete obstruction forPto be an asymptotic prime divisor ofMwith respect to the integral closure filtration, allowing us to employ a theorem of McAdam as a bridge to analytic s

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Dissertations / Theses on the topic "Powers of monomial ideals"

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Gasanova, Oleksandra. "Properties of powers of monomial ideals." Licentiate thesis, Uppsala universitet, Algebra och geometri, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-410846.

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Epstein, Melker. "Powers and Products of Monomial Ideals." Thesis, Uppsala universitet, Algebra och geometri, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298044.

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Coughlin, Heather. "Classes of normal monomial ideals /." view abstract or download file of text, 2004. http://wwwlib.umi.com/cr/uoregon/fullcit?p3147816//.

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Thesis (Ph. D.)--University of Oregon, 2004.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 85-86). Also available for download via the World Wide Web; free to University of Oregon users.

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Altafi, Nasrin. "Lefschetz Properties of Monomial Ideals." Licentiate thesis, KTH, Matematik (Inst.), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-223373.

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This thesis concerns the study of the Lefschetz properties of artinian monomial algebras. An artinian algebra is said to satisfy the strong Lefschetz property if multiplication by all powers of a general linear form has maximal rank in every degree. If it holds for the first power it is said to have the weak Lefschetz property (WLP). In the first paper, we study the Lefschetz properties of monomial algebras by studying their minimal free resolutions. In particular, we give an afirmative answer to an specific case of a conjecture by Eisenbud, Huneke and Ulrich for algebras having almost linear

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Àlvarez, Montaner Josep. "Local cohomology modules supported on monomial ideals." Doctoral thesis, Universitat de Barcelona, 2002. http://hdl.handle.net/10803/657.

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Sigui R l'anell de polinomis amb coeficients en un cos k de característica zero. El nostre objectiu és, tot seguint la linia de recerca encetada per G. Lyubeznik, utilitzar en profunditat la teoria de D-mòduls per tal d'estudiar els mòduls de cohomologia local de R amb suport un ideal I. En especial, ens interessa descriure de forma efectiva l'anul.lació, les propietats de finitud i entendre millor l'estructura d'aquests mòduls. La principal eina que utilitzarem és un invariant que podem associar als mòduls de cohomologia local i més en general a tot D-mòdul holònom: el cicle característic.<br

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Bruynooghe, Daniel. "Differential cumulants, hierarchical models and monomial ideals." Thesis, London School of Economics and Political Science (University of London), 2011. http://etheses.lse.ac.uk/441/.

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Crispin, Quiñonez Veronica. "Integral closure and related operations on monomial ideals /." Stockholm : Department of Mathematics, Stockholm University, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-770.

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Goward, Russell A. "A simple algorithm for principalization of monomial ideals /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3012972.

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Shokrieh, Farbod. "Divisors on graphs, binomial and monomial ideals, and cellular resolutions." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/52176.

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We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs. We use ideas from potential theory on graphs and from the theory of Delaunay decompositions for lattices to describe their minimal polyhedral cellular free resolutions. We show that the resolutions of all these ideals are closely related and that their Z-graded Betti tables coincide. As corollaries, we give conceptual proofs of conjectures and questions posed by Postnikov and Shapiro, by Manjunath and Sturmfels, and by Perkinson, Perlman, and Wilmes. Various other results rela

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Zheng, Xinxian. "Homological properties of monomial ideals associated to quasi-trees and lattices." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972174532.

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Books on the topic "Powers of monomial ideals"

1

Takayuki, Hibi, and SpringerLink (Online service), eds. Monomial ideals. Springer Verlag, 2011.

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Herzog, Jürgen, and Takayuki Hibi. Monomial Ideals. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-106-6.

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Bigatti, Anna M., Philippe Gimenez, and Eduardo Sáenz-de-Cabezón, eds. Monomial Ideals, Computations and Applications. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38742-5.

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Moore, W. Frank, Mark Rogers, and Sean Sather-Wagstaff. Monomial Ideals and Their Decompositions. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-96876-6.

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Carlini, Enrico, Huy Tài Hà, Brian Harbourne, and Adam Van Tuyl. Ideals of Powers and Powers of Ideals. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45247-6.

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Dark side: The inside story of how the war on terror turned into a war on American ideals. Doubleday, 2008.

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7

Mayer, Jane. Dark side: The inside story of how the war on terror turned into a war on American ideals. Doubleday, 2008.

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8

Mayer, Jane. The dark side: The inside story of how the War on Terror turned into a war on American ideals. Anchor Books, 2009.

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The dark side: The inside story of how the War on Terror turned into a war on American ideals. Anchor Books, 2009.

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Mayer, Jane. The dark side: The inside story of how the War on Terror turned into a war on American ideals. Anchor Books, 2009.

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Book chapters on the topic "Powers of monomial ideals"

1

Herzog, Jürgen, and Takayuki Hibi. "Powers of monomial ideals." In Monomial Ideals. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-106-6_10.

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2

Francisco, Christopher A., Huy Tài Hà, and Jeffrey Mermin. "Powers of Square-Free Monomial Ideals and Combinatorics." In Commutative Algebra. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-5292-8_11.

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Fouli, Louiza, Huy Tài Hà, and Susan Morey. "Depth of Powers of Squarefree Monomial Ideals (Research)." In Advances in Mathematical Sciences. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42687-3_10.

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Carlini, Enrico, Huy Tài Hà, Brian Harbourne, and Adam Van Tuyl. "Associated Primes of Powers of Squarefree Monomial Ideals." In Lecture Notes of the Unione Matematica Italiana. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45247-6_2.

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Gimenez, Philippe, José Martínez-Bernal, Aron Simis, Rafael H. Villarreal, and Carlos E. Vivares. "Symbolic Powers of Monomial Ideals and Cohen-Macaulay Vertex-Weighted Digraphs." In Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-96827-8_21.

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Engström, Alexander. "Decompositions of Betti Diagrams of Powers of Monomial Ideals: A Stability Conjecture." In Springer INdAM Series. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20155-9_8.

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Hoşten, Serkan, and Gregory G. Smith. "Monomial Ideals." In Computations in Algebraic Geometry with Macaulay 2. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04851-1_5.

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Herzog, Jürgen, and Takayuki Hibi. "Monomial Ideals." In Monomial Ideals. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-106-6_1.

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Herzog, Jürgen, and Takayuki Hibi. "Shifting theory." In Monomial Ideals. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-106-6_11.

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Herzog, Jürgen, and Takayuki Hibi. "Discrete Polymatroids." In Monomial Ideals. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-106-6_12.

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Conference papers on the topic "Powers of monomial ideals"

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Hoa, Le Tuan. "Powers of Monomial Ideals and Combinatorics." In 3rd International Congress in Algebras and Combinatorics (ICAC2017). WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811215476_0012.

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SÁENZ-DE-CABEZÓN, Eduardo, and Henry P. WYNN. "Algebraic Reliability Based on Monomial Ideals: A Review." In Harmony of Gröbner Bases and the Modern Industrial Society - The Second CREST-CSBM International Conference. World Scientific Publishing Co. Pte. Ltd., 2012. http://dx.doi.org/10.1142/9789814383462_0018.

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Milowski, R. Alexander. "Computing irredundant irreducible decompositions of large scale monomial ideals." In the 2004 international symposium. ACM Press, 2004. http://dx.doi.org/10.1145/1005285.1005320.

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Roune, Bjarke Hammersholt. "A Slice algorithm for corners and Hilbert-Poincaré series of monomial ideals." In the 2010 International Symposium. ACM Press, 2010. http://dx.doi.org/10.1145/1837934.1837961.

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